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Description
The probabilistic appearance of the dependence of the breakdown voltage (electrical strength) of a dielectric located between the circles of a capacitor on the thickness in homogeneous and inhomogeneous fields for dielectric layers in the range from 0.1 mm to atomic thickness is considered. The results of already known experiments and an analytical view of the probability density of their distribution applied to the presentations of the probability integral and its averaging have been used in the work.
There are a lot of problems when it becomes necessary to deal with bodies of elementary dimensions (here we consider elementary sizes from 0.1 mm to 10-7 mm). Such an example is a thermal element in the inductive thermal sensors [1,2], or a spring installed in an inductive sound sensor, or a dielectric layer of used in microcircuits [3]. Therefore, there is a need to study the deviations of the corresponding physical quantities and the presentation of values and views for use in the micro range. To conduct a similar study of the corresponding physical value in this paper, let's introduce a probabilistic distribution function, the notion of its average value, and investigate the probabilistic deviation of the corresponding physical values. Our task is to introduce a probabilistic density distribution function p (Ei) corresponding to a physical value (for example, the electrical strength Ei) at each point (at least 10-7 mm) of every elementary volume, so that the physical value for that volume is defined as:
(E_0 ) ̅=(∫(E_0-∆E)^(E_0+∆E)▒〖ρ((Ei),) Ei dEi〗)/(∫(E_0-∆Ei)^(E_0+∆E )▒〖ρ((Ei)) d〗 Ei), where Eo is the probable value of the electrical strength; ∆E – the possible deviation from electrical strength.
